I have a song I like to sing inside my head when I'm using the communal changing rooms at the swimming pool. It's usually inspired by spotting some poor woman go through hideous contortions to get her clothes back on without ever being fully unclothed, and it goes like this: "Get your tits out, get your tits out … " – it's based on a traditional folk song – " … get your tits out for the love of God woman, and stop clasping a wet towel around yourself while you put your bra on, you've flashed your nipples three times trying to do up the hook and eye one-handed."

Britons are spectacularly bad at being naked. I was reminded of this on Friday when I spotted Victoria Coren (dressed) on Room 101, consigning "people who are naked in public changing rooms" to her own personal hell. This seemed a little unfair, like hating on people who eat in restaurants or piss in public toilets: you don't have to love the bare flesh, or the chomping jaws, or the fizz of urine against porcelain, but at least accept that this is the least worst place for it to happen. Society has drawn a line around this room and said: "This is the place in which you may get changed." If we can't be undressed there, then where in the name of gooseflesh and armpit stubble can we?

The answer for a lot of people is nowhere, thank you very much. We are a nation of never nudes. The tragedy is, no one is ever as helplessly exposed as when conducting the dance of the seven veils with a pair of knickers and a soggy bath sheet. This came to me as an epiphany in the changing room of Butlin's Splash Waterworld, Minehead, during a music festival that attracted a mix of ultra-indie Brits and super-cool Euro types. Like the rest of my countrywomen, I struggled through the awkward routine of dignity preservation I'd learned at school – right hand to left hip, left hand shielding right boob, trying to hoik my straps with my elbows.

Meanwhile, the Euro girls had stepped clean out of their skinny jeans, into their bikinis and circuited the lazy river three times. And even with their clothes off, they'd never seemed half as naked as those of us twisting our part-dressed bodies against the mortal terror of being seen. Right then, I decided that the whole naked-shame thing was a swizz: a complicated, time-consuming means not of covering up but of saying sorry for having the awful temerity to have a body. "Sorry I've got these tits, I know they're supposed to be bigger. And perkier. Sorry about the stretch marks. Sorry about my pubic hair, I meant to trim it, but you know, busy!"

This isn't just paranoia. There really are people who expect everyone else to be in a state of permanent grovelling apology for their corporeal existence. These people are the keepers of the circle of shame that embraces the dimples on size 6 thighs like a halo and raises them to the cover of Closer for our religious contemplation. They're the ones for whom the words "flaunt" and "curves" are a single linguistic unit – because if you've got any more than the minuscule quantity of flesh deemed acceptable, the existence of your body is a society-defying display.

They're the ones like the New York Post critic who watched Lena Dunham in Girls and could think of nothing to say about the show because she was so mesmerised by Dunham's "giant thighs, sloppy backside and small breasts" – and the fact that these were presented as non-repulsive. Imagine! A perfectly normal, cute young woman having sex! The absurdity! If everyone who didn't look like the lovely Anne Hathaway were disgusting to potential partners, then humanity would be facing extinction. Instead, women of all body types manage to pull all the time, because women of all body types are fanciable.

You can learn this lesson from watching amateur porn if you like, but the nice thing about changing rooms is that people aren't naked just for sexual gratification. In a changing room, bodies are between business, just being. And you can look along the benches at your fellow changers … Well, no, you can't, because that would be creepy. But you can be conscious of them out of the corner of your eye, as you make your own transition from clothed to naked and back to clothed, and you can think: "So that is a normal body. That's all right then."